Overview

This document records the generation of cost surfaces from mean frequency maps for the Liverpool Bay area. The cost rasters are generated using the new data obtained.

Purpose

The purpose of this document is to record the process adopted to generate mean and most common rasters for use in the linkage between SWAT and Forel-Ule. The requirement is:

  1. A raster for each month of the year with the mean class value across the 2017 to 2021 period.
  2. A raster for each month of the year with the frequency of the most common Forel-Ule class for each cell across the period 2017 to 2020.
  3. A raster for each month of the year with the maximum class value observed across the 2017 to 2020 period.
  4. A raster for each month of the year with the frequency of the Forel-Ule class exceeding the mean for each cell across the period 2017 to 2020.

The plots show the frequency of the maximum Forel-Ule value, and water quality class (1-4; Citclops) for the period 2017-2020 for Jan to Dec.

Mean FU class observed in each cell each month

These rasters give the mean FU class value for each cell per month over the period 2017-2021.

The Mean Forel-Ule class rasters

Here the FU classes rasters mean values are plotted. Here for plume 1.

And here as seasonal means (these are the mean value of ALL the rasters within that season in the period 2017 to 2021.

These rasters are saved.

The Mean Forel-Ule class rasters - Plume 2

Here the FU classes rasters mean values are plotted. Here for plume 2.

And here as seasonal means (these are the mean value of ALL the rasters within that season in the period 2017 to 2021.

These rasters are saved.

## Warning: package 'av' was built under R version 4.1.3

Cost Functions linking the Forel-Ule class to the presence of DIN

An empirical approach was taken to link the Forel-Ule class to the presence of DIN in the water. The water quality data uwas new data and was used to create a local polynomial regression fit between the Forel-Ule class and the concentration of nitrate, nitrite and ammonium in the water. To do so a fit was performed using the LOESS function for readings for “Nitrate and Nitrite” and for “Ammonium”. The polynomial fitting is shown in the figure below.

Loess fit for NOx

Loess fit for NH4

The cost functions were normalised to a 0.1-0.9 scale with 0.1 representing the highest exposure (in both cases class 21). To calculate the normalised function for DIN, the predicted concentrations for each Forel-Ule class was summed and then normalised against the summed values.

And here as a table of values:

FUI NormCost
1 0.90
2 0.90
3 0.90
4 0.90
5 0.90
6 0.90
7 0.90
8 0.90
9 0.90
10 0.90
11 0.89
12 0.88
13 0.87
14 0.86
15 0.82
16 0.74
17 0.58
18 0.40
19 0.25
20 0.14
21 0.10

Using the normalised cost values based on primary, secondary and tertiary FUIs

In this section we are using the normalised cost values that are 0.9 for the tertiary waters (FUI 1 to 9), and LOESS correlation prediction for a combination of Nitrate+Nitrite and Ammonium for FUI 10 to 21.

A plot of these cost surfaces is shown below: